In the context of the financial value ascribed to the ability to holdoff on deciding whether to make an investment, Jensen's inequality hasbeen used to describe the fact that the average of the maximum returnsfrom several possible future outcomes is greater than the maximum ofthe average returns for those same set of possible future outcomes.This is because (apparently) the max function is convex. However,I've only seen Jensen's inequality described in terms of a functionthat takes one input argument and returns one output argument i.e. atransformation of the outcomes values of a random variable. The maxfunction is not like that. So it's not possible to plot the maxfunction as output value versus input value. For this reason, thejustification for calling the max function convex eludes me. In whatsense is the max function convex?